Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
430 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×#638 | C2 | semidirect |
| 2. C2×C3×C5×#67 | C2 | semidirect |
| 3. C2×C5×#626 | C2 | semidirect |
| 4. C2×C5×#624 | C2 | semidirect |
| 5. C3×C5×#217 | C2 | semidirect |
| 6. C5×Dic3⋊Dic3 | C2 | semidirect |
| 7. C5×(C2×D3)⋊Dic3 | C2 | semidirect |
| 21. #63958 | C5 | direct (N × H) |
| 27. C2×C5×#67 | D3 | semidirect |
| 33. C5×#217 | D3 | semidirect |
| 43. C2×C5×C3⋊D3 | D4 | semidirect |
| 50. C3×C5×Dic3 | D4 | semidirect |
| 52. C2×#638 | C2×C5 | semidirect |
| 53. C2×C3×#67 | C2×C5 | semidirect |
| 54. C2×#626 | C2×C5 | semidirect |
| 55. C2×#624 | C2×C5 | semidirect |
| 56. C3×#217 | C2×C5 | semidirect |
| 57. Dic3⋊Dic3 | C2×C5 | semidirect |
| 58. (C2×D3)⋊Dic3 | C2×C5 | semidirect |
| 146. C5×Dic3 | #67 | semidirect |
| 152. C2×#67 | C5×D3 | semidirect |
| 158. #217 | C5×D3 | semidirect |
| 162. C32×C5 | #121 | semidirect |
| 180. C2×C3⋊D3 | C5×D4 | semidirect |
| 187. C3×Dic3 | C5×D4 | semidirect |
| 260. C3×C5 | #884 | semidirect |
| 261. C3×C5 | #938 | semidirect |
| 297. Dic3 | C5×#67 | semidirect |
| 304. C32 | C5×#121 | semidirect |
| 333. C5 | #63958 | direct (N × H) |
| 349. C3 | C5×#884 | semidirect |
| 350. C3 | C5×#938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#638 | 2 |
| C2×C3×C5×#67 | 2 |
| C2×C5×#626 | 2 |
| C2×C5×#624 | 2 |
| C3×C5×#217 | 2 |
| C5×Dic3⋊Dic3 | 2 |
| C5×(C2×D3)⋊Dic3 | 2 |
| C5×#938 | 3 |
| C5×#884 | 3 |
| #63958 | 5 |